Exercise Sheet 7
Q1. Consider the following transportation problem.
B1 B2 B3 B4
Find a basic initial feasible solution using each of the following algorithms:
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(i) North-West Corner method. (ii) Least Cost method.
(iii) Vogel’s method.
Q2. Solve the following transportation problem starting with the given basic feasible solution.
Q3. Take the optimal solution from Q2, and show that it is optimal by setting u1 = ↵ rather than u1 = 0, and hence explain why it is always su cient to set u1 = 0.
Q1 We state the solutions. Note that in some cases other solutions are also acceptable since we may have to make arbitrary choices.
B1 B2 B3 B4
B1 B2 B3 B4
A2 10 A3 3
B1 B2 B3 B4
Q2 We solve as follows:
15 662 565 02
45 662 232 02
This table is dual feasible and hence optimal.
Q3 We have:
↵+2 ↵+3 ↵+2 ↵2
↵+1 7 ↵+1 5
Since whenever we compute vj ui the ↵ vanishes, it does not matter what value we take for ↵. Hence we may take ↵ = 0.
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